A Study on the Estimation Method of Extreme Wave Height Taking Sea State Persistence into Account

无论是波高和风速的极值，还是波高和风速在阈值以上的持续时间，都是海岸建筑物设计和海岸防御工程规划中需要考虑的重要因素，但由于缺乏高质量的长期数据，进行的尝试很少。本研究对日本沿海及周边海域多个观测点收集的长期波高、风速资料进行了详细的统计分析。提出了以波高或风速数据的无量纲方差及其无量纲阈值为自变量的回归模型，用于估计长期波高或风速的概率分布及其在持续期内持续超过某一阈值和峰值的概率分布。将上述三种回归模型结合起来，对持续时间超过阈值的大浪或大风的重现期进行了估算。其次，对概率分布的参数估计采用何种拟合方法以获得可靠的统计量估计，以及如何评估抽样变异性进行了研究。研究使用了威布尔分布、冈贝尔分布等8种理论概率分布和概率加权矩方法、极大似然法等4种参数估计方法。在对蒙特卡罗模拟技术产生的数据用3种或4种方法进行统计分析的基础上，从最小化统计偏差和方差的角度，为每种分布确定了参数估计的最佳方法。并验证了刀切法和信息矩阵法在统计方差估计中的适用性。

Not only extremes of wave height and wind speed but also persistences of wave height and wind speed above a threshold value are important factors to be considered in design of coastal structures and planning of coastal defense works, but few attempts have been conducted because of lack of long term data with good quality. In this study, detail statistical analyzes have carried out for the long term data of wave height and wind speed gathered at many observation points around the coasts of Japan and the surrounding sea area. Regression models, in which independent variables are the dimensionless variance of the wave height or wind speed data and its dimensionless threshold value, are proposed for the estimation of probability distribution of long term wave height or wind speed and probability distributions of its persistence above a threshold and peak value during the duration period. Return period of high waves or strong winds with duration above a threshold, where these values are prescribed is evaluated with the combination of the above-mentioned three regression models. Next, an investigation has been made to find what kind of fitting method is preferable for the parameter estimation of a probability distribution to obtain a reliable estimate of statistics and how the sampling variability could be evaluated. The study uses 8 kinds of theoretical probability distribution including the Weibull and Gumbel distributions and 4 kinds of parameter estimation methods such as the probability weighted moment method and maximum likelihood method. Based on the statistical analysis with use of 3 or 4 methods for data generated by a Monte-Carlo simulation technique, the optimum method to be used for parameter estimation was determined for each distibution from the view points of minimizing bias and variance of statistics. Also applicability of the jackknife method and information matrix method to the estimation of variance of statistics were verified.